Socrates refers to the divine ear, if I recall correctly, as his "daimonion." That word does not have the connotation of our modern English word "demon," but the meaning in ancient Greek is closer to "deva," or "divine," so I believe it translates as "divine ear."
In The Apology, Socrates explains that he listens to his daimonion in all things, and that it is what guides him to behave as he does at his trial. On another occasion, when Socrates has the opportunity to escape from his sentence in the Crito, he cites his daimonion as the reason why he does not. (Finally, I believe his premonition of his fate after death in the Crito, "that he will go to the land of Phthia," is also a result of his daimonion.)
One of the discussions I had with Jhanananda recently was about the topic of "revealed knowledge." I think that in reference to the trial and his escape, the daimonion is very closely tied to this phenomenon. In this way, we can see it as an Inner Voice. But, at the same time, I do not think what Socrates is referring to is at all different from divine hearing, as well.
To go further, I think it is very worthwhile to return to Plato with a mature, mystical perspective. Often, modern scholars do not see the mysticism of Socrates. I personally have become absolutely convinced of the mysticism of both Socrates and Plato, but especially Socrates.
It is interesting how a contemporary philosophy professor might read Socrates' long discussions of metempsychosis in a way very different from how we might. He might gloss over it, not read it literally, or not understand it in the way in which it was intended to be read. Aside from that, we have other signs of Socrates' attainment, in his discussions of love, his trances, and so on.